January 5, 1893] 



NATURE 



227* 



In Sir A. Geikie's calculation and all other similar ones with 

 which I am acquainted, the thickness of the sedimentary rocks 

 is tacitly assumed to be their thickness all over the land area of 

 the globe. 



Dr. Wallace's calculation leads to the absurd result that con- 

 tinents are growing nineteen limes as fast as materials are 

 produced to supply their growth. 



Leaving the question of the conclusions to which Dr. Wal- 

 lace's data logically lead, I may say that I am not responsible, 

 and do not hold him to be responsible, for the absurd theory 

 as to the thickness of sedimentary rocks on which they are 

 based. ", 



In order to arrive at a scientifically accurate results what we 

 require to know is the present actual thickness in every part of 

 the world, plus all the thickness which has previously existed in, 

 but since been denuded away from, every area. The existing 

 thickness in geologically explored areas can perhaps be ascer- 

 tained within certam limits of error from geological maps and 

 memoirs. For instance where the surface consists of Torridon 

 Sandstone overlying Arcbcean gneiss of igneous origin, the 

 thickness of sedimentary rock is that of the Torridon Sandstone 

 only, if we assume that the gneiss there is part of the metamor- 

 phosed original crust of the earth, for the existence of which 

 Rosenbusch has recently argued. 



It is easily demonstrable, first, that in many places the 

 existing thickness of each formation, where undenuded, is far 

 from being the maximum thickness, and, secondly, from the 

 thinning out in some directions, or merging, near the old shore- 

 line, into conglomerates, that some formations were never de- 

 posited over certain area> ; indeed, the very existence of a 

 sedimentary deposit necessarily implies that of land undergoing 

 denudation and not receiving deposit, although it may well be 

 doubted whether the land area was always nineteen times the 

 area receiving deposit. 



Reasoning from the deposits preserved as to those removed by 

 denudation, it is highly improbable that any considerable area 

 ever received either the complete series of deposits, or on the 

 average anything like the maximum thickness of the deposits it 

 actually received. In addition to this, some formations usually 

 considered to be succes.-ive may be really contemporaneous, 

 so that the figures representing maximum thicknesses usually 

 taken in calculating the earth's age are probably far above the 

 truth for the purpose in question. 



The immense labour involved in calculating the existing 

 thickness of sedimentary rocks in each area, and the thick- 

 ness which there is any reasonable ground for supposing to 

 have been at any time denuded from that area, as well as 

 the uncertainty of the results, has probably deterred geologists 

 from attempting the task, especially as large areas are very im- 

 perfectly known. Bernard Hobson. 



Tapton Elms, Sheffield, December 24. 



The first part of Mr. Hobson's letter alone requires notice 

 from me, as the latter part characterizes as absurd the views of 

 those eminent geologists who have estimated the total thickness 

 of the sedimentary rocks, and seems to assume that such 

 writers as the late Dr. Croll and Sir Andrew Ramsay overlooked 

 the very obvious considerations he sets forth. 



As regards myself, he reiterates the statement that when 

 geologists have estimated the total thickness of the sedimentary 

 rocks at 177,200 feet, they mean that this amount of sediment 

 has covered the whole land surface of the globe ; that, for 

 example, the coal measures, the lias, the chalk, the greensand, 

 the London clay, &c., &c., were each deposited over the whole 

 of the continents, since it is by adding together the thicknesses 

 of these and all other strata that the figure 1/7,200 feet (equal 

 to 33 miles) has been obtained. 



Mr. Hobson concludes with what he seems to think is a 

 rcductio ad ahsurdiim .— " Dr. Wallace's calculation leads to the 

 absurd result that continents are groAfing nineteen times as fast 

 as materials are produced to supply their growth." 



But the apparent absurdity arises from the absence of any 

 definition of the "growth of continents," and also from sup- 

 posing that the growth of continents is the problem under dis- 

 cussion. The question is, as to the growth in thickness, of sedi- 

 mentary deposits such as those which form the geological series. 

 These deposits are each laid down on an area very much smaller 

 than the whole surface of the continent from the denudation of 

 which they are formed. They are therefore necessarily very 



NO. I 2 10, VOL. 47] 



much thicker than the average thickness of the denuded layer, 

 and the ratio of the area of denudation to the area of deposition,, 

 which I have estimated at 19 to i, gives their proportionate 

 thickness. If Mr. Hobson still maintains that he is right, he 

 can only prove it by adducing evidtnce that every component of 

 the series of sedimentary rocks has once covered the whole land- 

 surface of the globe ; rfot by assuming that it has done so, and 

 characterizing the teaching of all geologists to the contrary as 

 absurd. Alfred R. Wallaci;. 



Ancient Ice Ages. 



Mr. Reade in his letter (Nature, p. 174) refers to the 

 striations on the pebbles forming the conglomerates at Abberley 

 and the Clent Hills. 



Following the late Sir Andrew Ramsay, he considers the 

 deposits to be of glacial origin, but goes further than that dis- 

 tinguished geologist in citing them as proof of a former ice 

 age. 



It is but reasonable to suppose that glaciers existed in past 

 ages in places where the conditions — such as high altitude and 

 abundant precipitation— were favourable. 



Before, however, the existence of a ioimcr glacial period can 

 be established, we must have evidence of contemporaneous 

 deposits of undoubtedly glacial origin, and extending over wide- 

 spread areas-t^say half a hemisphere. J. I-OMAS. 



University College, Liverpool, December 31. 



Printing Mathematics. 



The use of the solidus in printing fractions has been advocated 

 by authorities of such weight that it seems almost a heresy to 

 call it into question. Yet I venture to think that there is a 

 good deal to be said against it. In such matters the course 

 preferred by mathematical writers and their printers is apt to 

 take precedence over that which is most convenient for the great 

 body of those who will read their work. It is tacitly assumed 

 by those who prefer this notation that the getting of mathema- 

 tical formulae into line with ordinary printing is an unmixed 

 advantage. No doubt it is easier to set up the work in type 

 thus, but with the consequent rapidity and cheapness of printing 

 the advantage ends. Most people will agree that it is much 

 pleasanter to read a mathematical book in which the letterpress 

 is well spaced, so that the formulae stand ouf clearly from the 

 explanatory language, than one in which the two run together 

 in an unbroken stream : just as a book divided into paragraphs 

 is more readable than one which is not. The old style is more 

 restful to the mind and eye, and one can more readily pick out 

 the salient features of the demonstration. 



Another aspect of the question seems to me more important. 

 In making any calculation mentally it is much easier to visualize 

 fractions, more especially if complicated, as written in the 

 ordinary way than as written with the new-fashioned notation. 

 The component parts of the mental picture are imagined as 

 spread over a plane instead of being arranged along a line, and 

 can be thought of separately with less confusion. From a 

 similar pomt of view it will be admitted that it is inconvenient 

 to write mathematical expressions in one form and to print them 

 in another. 



Then, again, I doubt whether the assumption that the solidus 

 notation conduces to accuracy is justified. No doubt the printer 

 makes fewer original errors ; but whereas with the old notation 

 his frequent glaring errorsaremorereadily detected by the proof- 

 reader (or, if missed by him, by the ordinary reader), with the 

 new notation the misplacement or omission of a solidus is, from 

 the simplicity of the error, likely to be overlooked. In general, 

 no one will be the poorer if a little more trouble is taken with 

 the printing, and a little more paper is used for the book. 



The symbol / has advantages over its equivalent -^, and to 

 its restricted use, such as is made by Sir G. Stokes, one can 

 hardly object ; it matters little how such expressions as a/b or 

 dy/dx are printed. But it is the thin end of the wedge; and one 

 is under a debt of gratitude to Mr. Cassie for showing, in your 

 issue of November 3, to what it may lead. May it be a long time 

 before we have to learn to substitute for the harmless expression, 



~id '" ^» ^'^ newest equivalent, | ^ \ i /z \ t c \ d ^ c\l\l 

 I trust that no one will interpret the final note of exclamation as 

 a factorial symbol. M. J. Jackson. 



D. I. Sind College, Karachi, November 23. 



